In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle).
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.
Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a rectangle by polygons.
Homework Statement
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.
Homework Equations
(x-a)^2 + (y-b)^2 = r^2
max area = 2x(2y)
= 4xy
The Attempt at a Solution
(x-a)^2 + (y-b)^2 = r^2
= y=r-(x-a)+b
I then plug...
Homework Statement
Largest possible area of a rectangle inscribed in the ellipse (x2/a2)+(y2/b2)=1
Homework Equations
Area of the rectangle = length*height
The Attempt at a Solution
I have it set up so that the four corners of the rectangle are at (x,y) (-x,y) (-x,-y) (x,-y) and that...
Homework Statement
A rectangle has sides on the x and y axes and a corner on the plane x+3y=12. Find its maximum area.
Homework Equations
A=xy=(12-3y)y
(A=12, according to the solution manual.)
The Attempt at a Solution
At first I thought the corner it was talking about lay...
1) Homework Statement [/b]
The surface density of a rectangle varies as:
σ(x,y)=12 kg/m2+2 kg/m4(x2+y2)
The origin is located at the lower left corner of the rectangle, at point ``A.'' The rectangle has a height h=1.00 m and a length l=1.20 m. What is the total mass of this object?
The Problem is finding the E-field at a point P that is h distance from the center of a rectangle (along a line normal to its surface) with Length L and width W with a constant charge density sigma.
This is for an intro E&M class that is supposed to use up through calculus 2, and we have not...
Homework Statement
Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions
u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0
Homework Equations
The Attempt at a Solution
I know that with...
Hi
Let's assume we have a, say, 10 cm * 20 cm, not very thick, rectangular object. We also have a huge ball, with a known radius of about 1 m. Now be put that rectangle onto the ball surface. What happens to the rectangle?
I know that a 2D-object doesn't fit very well onto a spherical...
Problem: What is the area of the largest rectangle that can be inscribed in the ellipse 9x2+4y2=36
Relevant Equations:
equation of an ellipse: (x - h)2/a2 + (y - k)2/b2 = 1
I only got as far as
x2/4 + y2/9 = 1
(x - 0)2/22 + (y - 0)2/32 = 1
I have no idea where to go from here
Hi,
If I have the equation for a plane, Ax+By+Cz+D=0, how can I find four points that represent a rectangle width w and length l on that plane? (assuming the given point on the plane is the center of that rectangle..)
Thanks..
[SOLVED] Optimization: Rectangle Inscribed in Triangle
Homework Statement
Please see http://www.jstor.org/pss/2686484 link. The problem I have is pretty much exactly the same as that dealt with in this excerpt.
(focus on the bit with the heading "What is the biggest rectangle you can...
[SOLVED] Moment of inertia of a sign consisting of ring and rectangle
Homework Statement
A sign is formed from two uniform discs,each of mass 0.25kg and radius 0.2m,rigidly,fixed to a uniform rectangular lamina ABCD at A and D. This dis attached at A has diameter AE and BAE is a straight...
This integral came up while trying to find the potential of a uniformly charged rectangle.
\int \log(\sqrt{a^2+x^2} + b) dx
Integrator gives a pretty long expression involving inverse tangents so I'm not sure where to begin at all. I tried integrating by parts once, taking u to be the...
Homework Statement
An isosceles triangle has base 6 and height 12. Find the maximum possible area of a rectangle that can be placed inside the triangle with one side on the base of the triangle.
Homework Equations
None.
The Attempt at a Solution
Well, so far I've created an X-Y...
Homework Statement
Heres a picture that might help
http://img132.imageshack.us/img132/3809/semirectanglexf6.png
A family wants to create that shape for basketball with duct tape, the family only has 20 ft of duct tape. The family decides they want to maximize the area of the...
An electron is confined to a rectangle with infinitely high walls.I need to calculate the ground state energy of the electron.
Can I treat a rectangle with infinite high walls to be the same as 2d box as mentioned here.
http://en.wikipedia.org/wiki/Particle_in_a_box
or it should be...
Homework Statement A rectangle is expanding so that its length is always twice its width. The perimeter of the rectangle is increasing at a rate of 6cm/min. Find the rate of increase of the area of the renctangle when the perimeter is 40 cm.
Homework Equations
The Attempt at a Solution
p = 6x...
The E-field at the center of 4 charges
You construct a rectangle that is 6cm by 8cm, and place the following four charges at each corner: 2mC, -4mC, 2mC, -3mC. The 2mC starts at the top left corner and then each is placed around the rectangle in order in a clockwise manner.
A) What is the...
The Problem:
To find the maximum area of a rectangle within the boundaries of an isosceles triangle with a base of 10 and congruent sides' lengths of 13.
How Far I Was Able to Get:
I was able to prove that the max area was 30 if one of the sides of the rectangle coincides with one of the...
Homework Statement
A plane is colored blue and red in any way . Prove that there exists a rectangle with vertices of the same color
Homework Equations
Its obviously true.
The Attempt at a Solution
I was thinking proofy by pig hole, but haven't quite figured it out.
Improper integral and "rectangle" method
If we have a definite integral then..using "rectangle" method we can get the approximation:
\int_{a}^{b}f(x)dx \sim \sum_{n=0}^{N}f(a+nh)h
My question is..how do you define this method when b-->oo (Imporper integral?)...:confused: :confused:
http://img424.imageshack.us/img424/6972/showmeks9.gif
Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.1 m, b = 0.7 m, q = 2.4 × 10-9C)?
So you need to break this into X and Y, for Hypotnuse i got 1.303
So wat i did...
Is it possible to transform an ellipse
x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis)
Into a rectangle?
If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.
Diagonals of a Rectangle?
Why don't the diagonals of a rectangle bisect the angles? This may seem so easy, but I'm having difficult time understanding it...I'm confused because I know that the digonals of a rectangle bisect each other...so then why don't the angles do the same? Pls. Help...
Here is the problem i am stuck on: There are 4 charges arranged in a rectangle pictured with side lengths .03m and .05m. The top 2 charges are negative and the bottom 2 charges are positive. All 4 charges have the same magnitude of 8.60*10^-12 C. Find the magnitude of the electric field at...
Heres where I am struggling, I can't seem to change equations from rectangular to polar and vice versa
an example
x^2+y^2-2ax=0
heres what I got when I tried
r=2a cos theta
and that's a graph of a rose curve, I think, I am about 10% sure on that answer
heres an example of one I...
Since things are a bit quiet here, I thought I would throw out a puzzle I came up with several years ago, after reading an article on connected sets:
Find two sets, P and Q, satisfying:
1) Both P and Q are completely contained in the (closed) rectangle in R2 with vertices at (1, 1)...
I have this question:
Positive charges are situated at 3 corners of a rectangle with charges q1, q2, and q3. Given each of their distances from the 4th corner of the rectangle, what is the electric field at the 4th corner?
Would it be the vector sum of the electric field of each of those...
Please Help Pre-Cal !
1.A rectangle has one vertex on the line y=L-Fx,x>0 , another at the origin, one on the positive x-axis, and one on the positive y-axis. Find the largest area A that can be enclosed by the rectangle. Show all your work and include a sketch with labels of all important...
Hey guys, here is a problem i have with the work i have done so far. I am not sure how to factor in the torque due to the mass. I also want to make sure i am doing this correctly. THanks
problem
Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.3 m, b = 0.8 m, q = 1.8 × 10-9C)?
HELP: Use Coulomb's law and superposition.
HELP: Superposition tells us that we can find the force on the positive charge by looking at the...
Problem:
I have a computer image of a grid "square" from an aviation chart. The "square" is actually approximately rectangular, but the left and right sides aren't quite parallel and the top and bottom sides are parallel but very slightly curved.
I will assume/pretend that the top and...
how do i find the area of a rectanglewith sides 400root of 400 raised continously to itself like x^x^x^..and 800root of 800 raised also to itself continouslylike y^y^y...
leave answer in whole number not exponent
The problem asks me to show that the maximum possible area for a rectangle
inscribed in a circle of radius R is 2R^2. It also gives a hint saying that I should first maximize the square of the area.
I set the problem up as xy = 2R^2. I decided to work on the left side and wrote it as x(2R)...
You have a linear function f(x)=-\frac{2}{3}x+4 where 0\leq x\leq 6 and 0\leq y\leq 4. What is the maximum area of a rectangle that has one side on the line of the function?
I know how to optimize this, I am just having trouble finding the equation for area of such a rectangle in terms of...
What are the dimensions of a rectangular plot with maxium area if the north and south sides cost twice as much to fence as the east and west sides and if you have $1000 to spend? East and west sides cost $10 per meter to fence.
i am now trying to figure out the electro-field around a rectangle waveguide. the refractive index of the waveguide is n1, which is larger than that of the cladding, namely n2, outside. we may regard the waveguide embeded in the cladding material.
as following shown, the waveguide...
Question 1: A 2cm x 3cm rectangle lies in the xz-plane. What is the electric flux through the rectangle if
E=(50i+100k) N/C
and
E=(50i+100j) N/C
Question 2:
A 1cm x 1cm x 1cm box is between the plates of a parallel-plate capacitor with two faces of the box perpendicular to E ...
A rectangular piece of paper spins rapidly about its longitudinal axis as it falls
through the air.It takes longer to reach the ground than other shapes of paper.Why is this given that it spends a lot of time edge on to the flow of air and so encounters less resistance from the air than a...
Hey
Id appreciate some help with these questions:
(A) \alpha,\beta are roots of the equation x^2 - 2lx + m = 0. Show that \alpha^2 + \beta^2 = 2(2l^2 - m). Express \alpha^4 + \beta^4in terms of l and m.
Ive shown that \alpha^2 + \beta^2 = 2(2l^2 - m), but I am having trouble figuring out...
A man 1.75 m tall walks at a rate of 2m/s toward a streetlight that is 10m above the ground, at what rate is the length of the shadow changing when he is 6m from the base of the light?
Don't know what to do. => Pythagorean?
#2: A rectangle with base an x-axis is inclined under y = 6 -...